Question: Express this quotient in scientific notation: ${\frac{1.000\times 10^{-5}} {5.0\times 10^{-4}}}$
Solution: Start by collecting like terms together. $= {\frac{1.000} {5.0}} \times{\frac{10^{-5}} {10^{-4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.20 \times 10^{-5\,-\,-4}$ $= 0.20 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.20$ is the same as $2.00 \div 10$ , or $2.00 \times 10^{-1}$ $ = {2.00 \times 10^{-1}} \times 10^{-1} $ $= 2.00\times 10^{-2}$